Fig. 1
Electron–phonon interaction and deformation potential. a, b Electron–phonon coupling matrix along high-symmetry lines. The coupling matrices are calculated along two different directions in the Brillouin zone for a longitudinal acoustic phonons and b optical phonons, respectively, with the initial electron state located at the conduction band edge (\({\mathbf{k}}_{\mathrm{X}} = (0,0,2{\mathrm{\pi }}/a)\), where α is the lattice constant) and the final electron in the same band (intra-band coupling). The insets in a and b illustrate the lattice distortions corresponding to acoustic and optical phonons. c, d Averaged deformation potential for acoustic and optical phonons. The deformation potentials are extracted as the slopes from a, b, for the two different directions (one is parallel with kX while the other is perpendicular), defined as \(\Xi _\parallel\) and \(\Xi _ \bot\). The deformation potential generally depends on the directional angle of the phonon state, but for simplicity we calculate averaged deformation potential defined as \(\bar \Xi = \Xi _\parallel ^{1/3}\Xi _ \bot ^{2/3}\)
